Lecture 17 RRDE

8/15/2019 Lecture 17 RRDE

1/7

Lecture 17.1 Hydrodynamic Methods

Rotated Disk Electrode Voltammetry RDEV

u l a t o r

C o n d u c

t o r

e l e c t r o d

e

f π ω 2=

ω in s-1, so f in rps revolutions

per second

r 1

“dead” or

diffusion laye

Laminar flow occurs up to a point, at too i! ω, we findtat tur"ulent flow occurs# $is is wen te value

e%ceeds te Reynold&

num"er for tat particular fluid wit a !iven kinematic

viscosity, ν, in cm' s-1#

2

1

v

r ω

3

11

−

−−

→→

=cm g d

scm g nv

( R e ) ' % 1

* +

o, ω sould "e ( ' 1*+ ν.r ', "ut oter limitations actuallyean ω / 1*** s-1 or f 1*,*** rpm#

n te low ω side, must rotate fast enou! to esta"lis constant,omo!eneous supply of material to electrode surface# ω 1* s-1

≅

*)??20(*2001.0~

3

2

12

C at viswhat C at scmisv

CN CH

O H

°°

−

23oise4

Look in $a"le 5#'#1


2/7


6f one applies a potential wic is tat needed to o"tain

mass-transport limited conditions, ten wat is i 7

consider8

- ydrodynamics

- diffusion

9y7

C

* x

δ

∗o

C

0 : n e

R

o n l y 0

p r e s e n

t

Recall tat δ is ;21.ω4#

o,

δ

oooo

t oo

DmC mnFAi

x

C nFADi

==

↓≈

∂∂=

∗ ;

),(

ow solve7 =s we did "efore e%cept incorporate ydrodynamics

=lso8

$wo Cases81# Reversi"le use

θ e%pression 2>ernst4'# ?efore reac @$ limit

and - irrev#

- Auasi-rev# E$ r%ns#

)(),0(

),(

)0,(

E F t C

C t C

C xC

o

oo

oo

=

=∞

=∗

∗

Real

profile

@ u s t s c a n

E s l o w

l y,

ν / 1 *

* m V s -

1


3/7

Lecture 17.3 Hydrodynamic Methods no iDL effects#

Case 18 Levic EAuation

Bnow8

Bnow8 Levic Layer ;6.1

62.0

2/1

6/13/1

2/16/13/2

lim

ω

ν δ

ω ν

D

C nFADi oo

=

= ∗−

f reaction is DC, ten ilim vs# ω1.' is linear wit ero intercept#

=lso if E$ reversi"le8

Levic plot

i

ii

n D

D

n E E

cl

o

Ro −

+

+= ′ ,

3/2

log059.0

log059.0

> o

d e p e n d e n

c e

o f w a v e s

a p e

o n ω E

en plot of E app

vs# will "e strai!t wit slope V ni

iil 059.0log =−

Case '=8 $otally irreversi"leF 0 only

?ut,k

f is ;2E

4 , so we denote tisk

f 2E

4#

9e call tis current iB and it is8

$is is te Binetic current#

o, at i! enou! - , we sould !et k 77 >0#

[ ]∗∗ −= R bo C k C k nFAi

( ) ∗= o ! C E nFAk i

( )

−−°=′

RT

E E F nk k

o

aα e"#

E 1.'

Gero


4/7

Lecture 17.$ Hydrodynamic Methods

E1

E' EH

EI2on i li

9e ave no E$ effects at -η,6rrev# Rev# for i, so we merely !et ilim

ic

: -

ia

o, if we could vary E and measure iB, we

could !et 77°k

E vs Ref

E$ effects

?-V . >o @$

@$ effects

Jes


5/7


[ ] RT F nk E k RT

F n

k E E k

E k C A F n

E C E nFAk

a

o

f

a

oo

f

i f o

app

o f

/e"#)( %&'?

ilo#elo,

.l*o i*terce#tget+*)(or-.l*lot

.+tet.,,,

*o %e.+t)(

1 i*terce#tgeteo,

η α

α

η

−=

−=

−

′

∗

∗

Case '?8 uasi Reversi"le for 0 and R

>ow we ave "ot k f and k b a function of n# $us, teBouteckK Levic plots do not ave same slope for various

3otentials 2η4#

3ro"lems @inimie errors "y usin! small potential ran!e

near te foot of te wave were i is not can!in! so drastically

( )[ ] RT E E nF k

i

i

i

i

o

al cl o

/e"#

1

1

1

,

1

,

′

−−

−°=

++

−=

α α α

;nc2E4 E$

@$7

D o t i s o n

y o u r

o w n#


6/7


RRDE

r '

r H

r 1

r 1 disk radius

r ' r 1 !ap

r H r ' widt of rin!≡≡

≡

2R4 Rin!

2D4 Disk

δR

δD

δR ) δD

$e collection Efficiency, N , is defined as

6t is a ;unction of electrode !eometry "ut is independent

of etc# if R is sta"le#

kcem

6f R G occurs, ten N e%ptl / N teo and N ) ;2ω4#

,,,, Roo D DC ∗

ω

R

i

i N −=


7/7


or RRDE Collection E%periments8

1# E Rin! is eld positive enou! so as to o%idie any R#

'# >o "ulk

H# E Disk is scanned#

I# i Disk is measured#

+# i Rin! is measured#

0,R R =

∗

C

iD,c 0 : ne R

E Rin!

iD,lim

: - E Disk vs# Re

iR,lim

R 0 : ne

iR,a

)(

14;293.0t+ble

+,7or

.ire+ctio+t+bleii )(

,

,

2/12/1

ω

ω α ω α

ω

F N RRDE

i

i

i

i D!"CA R

iiC D

C D R F ii N

c p

a p

F

r

R D

D

R

≠

==−

−

−≠−=

Review8

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Lecture 17 RRDE